According to research that's supposed to be published later this year, growing demand for Internet use will soon outstrip the stamina of the infrastructure supporting it, and the Internet will cease to be reliable by 2012. Complete anarchy will ensue, and the world will essentially end along with the Internet we created for it. Perhaps this is what the Mayan prophecies meant?

This wont happen. As soon as IPv4 gets depleted, ISP will start to rush for IPv6. IPv6 is way better implemented than v4 and transport layer should cope better with the bandwith. Most of backbones today run on something else than IPv4 because it's simply unable to cope with the such high demand. All of this is the fault of TCP

By the time Internet2 should be out too. And I expect fiber to spread wider. Also, the current ISP interconnexion scheme may change. Currently most ISP are running in a reversed-tree like infrastructure. There is a need for more interconnect between ISPs. The initial Internet design was meant to be a graph, not a tree. The more interconnect there will be, the more the network will be efficient (just like a brain).